Scilab Function
Last update : Dec 1997

cdff - cumulative distribution function F distribution

### Calling Sequence

  `[P,Q]=cdff("PQ",F,Dfn,Dfd)`
  `[F]=cdff("F",Dfn,Dfd,P,Q);`
  `[Dfn]=cdff("Dfn",Dfd,P,Q,F);`
  `[Dfd]=cdff("Dfd",P,Q,F,Dfn)`

### Parameters

- `P,Q,F,Dfn,Dfd`: five real vectors of the same size.
- `P,Q (Q=1-P)` : The integral from 0 to F of the f-density. Input range: [0,1].
- `F`: Upper limit of integration of the f-density. Input range: [0, +infinity). Search range: [0,1E300]
- `Dfn`: Degrees of freedom of the numerator sum of squares. Input range: (0, +infinity). Search range: [ 1E-300, 1E300]
- `Dfd`: Degrees of freedom of the denominator sum of squares. Input range: (0, +infinity). Search range: [ 1E-300, 1E300]

### Description

Calculates any one parameter of the F distribution given values for the others.

Formula 26.6.2 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to reduce the computation of the cumulative distribution function for the F variate to that of an incomplete beta.

Computation of other parameters involve a seach for a value that produces the desired value of P. The search relies on the monotinicity of P with the other parameter.

The value of the cumulative F distribution is not necessarily monotone in either degrees of freedom. There thus may be two values that provide a given CDF value. This routine assumes monotonicity and will find an arbitrary one of the two values.

From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. The University of Texas.